# Optimal Subsampling Algorithms for Big Data Regressions

arXiv: https://arxiv.org/abs/1806.06761 · HTML: https://mlsanity.com/paper/1806.06761/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2018.

## Built on by (most cited first, 11 of 11)

- [Towards a statistical theory of data selection under weak supervision](https://mlsanity.com/paper/2309.14563/) (2023)
- [An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation](https://mlsanity.com/paper/2206.01182/) (2022)
- [Train on Validation (ToV): Fast data selection with applications to fine-tuning](https://mlsanity.com/paper/2510.00386/) (2025)
- [General bounds on the quality of Bayesian coresets](https://mlsanity.com/paper/2405.11780/) (2024)
- [Enhancing Semi-Supervised Learning via Representative and Diverse Sample Selection](https://mlsanity.com/paper/2409.11653/) (2024)
- [Data subsampling for Poisson regression with pth-root-link](https://mlsanity.com/paper/2410.22872/) (2024)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)
- [Backbone Augmented Training for Adaptations](https://mlsanity.com/paper/2506.04288/) (2025)
- [Core-elements Subsampling for Alternating Least Squares](https://mlsanity.com/paper/2509.18024/) (2025)
- [Scale-invariant Optimal Sampling for Rare-events Data with Sparse Models](https://mlsanity.com/paper/2608.22597/) (2026)
- [Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification](https://mlsanity.com/paper/2610.19351/) (2026)

## Abstract (arXiv)

To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the estimator from a general subsampling algorithm are established, and optimal subsampling probabilities under the A- and L-optimality criteria are derived. Furthermore, using Frobenius norm matrix concentration inequalities, finite sample properties of the subsample estimator based on optimal subsampling probabilities are also derived. Since the optimal subsampling probabilities depend on the full data estimate, an adaptive two-step algorithm is developed. Asymptotic normality and optimality of the estimator from this adaptive algorithm are established. The proposed methods are illustrated and evaluated through numerical experiments on simulated and real datasets.